Say that a polynomial in an indeterminate $x$ with real coefficients of degree $d$ *has positive coefficients* if each of the coefficients of $x^d,\ldots,x^1,x^0$ is (strictly) positive. 

For $f$ a **monic** univariate polynomial with real coefficients, if there exists a positive integer $m_0$ such that its $m_0$th power $f^{m_0}$ has positive coefficients, then does there exist a positive integer $m_1$ such that for each positive integer $m$ at least $m_1$, the $m$th power $f^m$ has positive coefficients?